Constructal Design and Simulated Annealing applied to the geometric optimization of an isothermal Double T-shaped cavity

Abstract

Present numerical work comprises the application of Constructal Design (CD) and Simulated Annealing (SA) for the geometric optimization of a Double T-shaped cavity inserted into a solid wall with internal heat generation. The main goal is to minimize the dimensionless maximum excess of temperature in the solid domain. The cavity is subjected to four constraints and five degrees of freedom (DOF). The Exhaustive Search (ES) and SA methods are employed to optimize the first three DOFs, validating the SA algorithm. From the fourth level onward, new recommendations about the design influence over the system's performance are reached, combining ES and different versions of SA. Results obtained showed the importance of investigating the influence of the DOFs over thermal performance, and corresponding design, using combined SA versions and ES. The proposed methodology reduced the computational effort in comparison with purely ES. For design investigation, the highest insertion of stem and branches led to the best performance. For square solid domains, the Double T-shaped cavity obtained an intermediate performance compared with I, T, Y, H, and ψ shapes. For small height/length solid domain ratios, the best shape found here performed several times better than the best configurations found in the literature.